Synthetic Single-Nanopore and Nanotube Membranes - Analytical

C. Chad Harrell, Youngseon Choi, Lloyd P. Horne, Lane A. Baker, Zuzanna S. ..... Youngseon Choi , Lane A. Baker , Heather Hillebrenner , Charles R. Ma...
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Anal. Chem. 2003, 75, 6861-6867

Synthetic Single-Nanopore and Nanotube Membranes C. Chad Harrell, Sang Bok Lee, and Charles R. Martin*

Department of Chemistry and Center for Research at the Bio/Nano Interface, University of Florida, Gainesville, Florida 32611-7200

There is increasing interest in investigating transport and electrochemical phenomena in synthetic membrane samples that contain a single pore of nanoscopic diameter. Approaches used to date for preparing such singlenanopore membranes include microfabrication-based methods, the track-etch method, and a method based on the incorporation of a single fullerene nanotube within a synthetic membrane. We describe here an alternative approach that we believe is easier and more accessible than the previously described methods. This method is based on a very low pore density track-etch membrane obtained from commercial sources. Fluorescence microscopy is used to identify and isolate a single nanopore in this membrane. Membrane samples containing single nanopores with diameters as small as 30 nm have been prepared. Furthermore, we show here that an electroless plating method can be used to deposit a gold nanotube within the single nanopore, and this provides a route for further decreasing the inside diameter of the pore. A single-nanotube membrane with an electrochemically determined inside diameter of ∼2 nm was prepared and evaluated. There is increasing interest in measuring and investigating transport and electrochemical phenomena in membrane samples that contain a single pore of nanoscopic diameter.1-6 One motivation for this interest stems from the fact that selective ion transport in nanopores (protein-based ion channels) is used throughout living systems for electrical signaling in nerves, muscles, and synapses.7 Very recent advances in making synthetic analogues of ion channels based on single-nanopore membranes are shedding light on the mechanisms by which these naturally occurring channels function.8-11 Another motivation for studying transport in single-nanopore systems comes from the work of Bayley et al., * Corresponding author. E-mail: [email protected]. (1) Howorka, S.; Movileanu, L.; Braha O.; Bayley, H. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 12996-13001. (2) Howorka, S.; Cheley, S.; Bayley, H. Nat. Biotechnol. 2001, 19, 636-639. (3) Gu, L.-Q.; Braha, O.; Conlan, S.; Cheley, S.; Bayley, H. Nature 1999, 686690. (4) Braha, O.; Gu, L.-Q.; Zhou, L.; Lu, X.; Cheley, S.; Bayley, H. Nat. Biotechnol. 2000, 18, 1005-1007. (5) Li, J.; Stein, D.; McMullan, C.; Branton, D.; Aziz, M. J.; Golovchenko, J. A. Nature 2001, 412, 166-169. (6) Deamer, D. W.; Branton, D. Acc. Chem. Res. 2002, 35, 817-825. (7) Hille, B. Ion Channels of Excitable Membranes, 3rd ed.; Sinauer Associates: Sunderland, MA, 2001; p 1. 10.1021/ac034602n CCC: $25.00 Published on Web 11/12/2003

© 2003 American Chemical Society

who have shown that measurements of the ionic current through a single-protein channel in a lipid bilayer membrane can form the basis of a new and versatile method for single-molecule chemical and biosensing sensing, called stochastic sensing.1-4 It has been recently shown that synthetic single-nanopore systems can also accomplish this single-molecule stochastic sensing function.5 As the above examples indicate, there has been considerable recent success in developing methods for preparing synthetic single-nanopore membranes. Approaches investigated to date include single-nanopore membranes prepared by microfabrication methods,5 by the track-etch method,8-11 and through incorporation of a single fullerene nanotube within a synthetic membrane.12 We have developed an alternative approach for making synthetic single-nanopore membranes that we believe is easier and more accessible than the previously described methods. This method is based on low pore density track-etch membranes obtained from commercial sources and is a derivative of a method described by Bean et al. in 1970.13 However, these authors made single-pore membranes where the pore diameter was quite large (>200 nm). Our method yields membranes with single nanopores having diameters as small as 30 nm, which can be subsequently decreased to ∼2 nm by depositing a gold nanotube within this pore.14-16 We describe this method for making synthetic singlenanopore membranes here. BACKGROUND Because the membranes investigated here are prepared by the track-etch method, we first briefly review this process. The tracketch method17 entails bombarding a solid material (in this case 12-µm-thick polycarbonate films) with a collimated beam of highenergy nuclear fission fragments to create parallel damage tracks (8) Siwy, Z.; Dobrev, D.; Neumann, R.; Trautmann, C.; Voss, K. Appl. Phys. A: Mater. Sci. Proc. 2003, 76, 781-785. (9) Apel, P. Y.; Korchez, Y. E.; Siwy, Z.; Spohr, R.; Yoshida, M. Nucl. Instrum. Methods Phys. Res., Sect. B 2001, 184, 337-346. (10) Siwy, Z.; Gu, Y.; Spohr, H. A.; Baur, D.; Wolf-Reber, A.; Spohr, R.; Apel, P.; Korchev, Y. E. Europhys. Lett. 2002, 60, 349-355. (11) Siwy, Z.; Mercik, S.; Weron, K.; Spohr, R.; Wolf, A.; Grzywna, Z. Acta Phys. Pol., B 2000, 31, 1125-1141. (12) Sun, L.; Crooks, R. M. J. Am. Chem. Soc. 2000, 122, 12340-12345. (13) Bean, C. P.; Doyle, M. V.; Entine, G. J. Appl. Phys. 1970, 41, 1454-1459. (14) Kobayashi, Y.; Martin, C. R. J. Electroanal. Chem. 1997, 431, 29-33. (15) Menon, V. P.; Martin, C. R. Anal. Chem. 1995, 67, 1920-1928. (16) Martin, C. R.; Nishizawa, M.; Jirage, K. B.; Kang, M. J. Phys. Chem. B 2001, 105, 1925-1934. (17) Fleischer, R. L.; Price, P. B.; Walker, R. M. Nuclear Tracks In Solids, Principles and Applications; University of California Press: Berkeley, CA, 1975.

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in the film. The damage tracks are then etched into monodisperse pores by exposing the tracked film to a solution of aqueous base. The diameter of the pores is determined by the etch time and the etch-solution temperature. The pore density (pores/cm2 of membrane area) is determined by the exposure time to the fissionfragment beam. Filtration membranes of this type with pore diameters ranging from as small as 10 nm to as large as 10 µm are sold commercially. These membranes have high pore densities, for example almost 109 pores cm-2 for the smallest porediameter commercial membranes. Bean et al. recognized over 3 decades ago that a single-pore version of such membranes would be technologically useful. They were interested in using such single-pore membranes as Coultertype counters13,18,19 for identifying and counting small particles, for example a bacteriophage with diameter of ∼100 nm.13 They obtained single pores by first preparing a low track density (∼103 tracks cm-2) membrane and then etching the tracks to make 250350-nm-diameter pores. A small square of this membrane was then cutout and mounted with epoxy over a 0.3-mm-diameter hole in a plastic disk. While the epoxy was still fluid, this sample was imaged under a 200-power stereomicroscope with dark-field illumination, through which the individual pores in the sample could be seen. The membrane square was moved around on the epoxy-coated disk until all of the pores except one were coated with epoxy, and the epoxy was allowed to harden. While quite innovative, the downside of this method is immediately obvious. Because the resolution of the light microscope is limited by the diffraction of visible light, the minimal single-pore diameter that can be achieved by this method is on the order of 200 nm. As will be discussed here, we have devised a fluorescence-based method that circumvents this limitation and allows for much smaller (e.g., 30 nm diameter) single-pore membranes to be prepared. Finally, there is an alternative track-etch method for preparing single-nanopore membranes.9,10 This method is based on a special tracking process in which a small area of the membrane to be tracked is isolated by a mask and placed between the heavy ion source and a silicon surface-barrier particle detector. When a single particle traverses through the membrane and is registered by the detector, an electromechanical shutter system switches the beam off, thus yielding a portion of the membrane with a single track, which can then be etched into a pore. A potential disadvantage of this method is that special tracking equipment is needed and these single-track membranes cannot be purchased commercially. In contrast, the membranes used here were obtained from commercial sources. Siwy et al. used this alternative single-pore track-etch method to prepare pores that were conically shaped, as opposed to the cylindrically shaped pores investigated here.10 They studied the potential dependence of the ion current in these single conical-pore membranes and showed that, in contrast to cylindrical pores, the conical pores show an interesting current rectification phenomenon; that is, the conical-pore membranes show nonlinear current voltage curves. We are currently also investigating this phenomenon in single conical-pore membranes. (18) DeBlois, R. W.; Bean, C. P.; Wesley, R. K. A. J. Colloid Interface Sci. 1977, 61, 323-335. (19) DeBlois, R. W.; Wesley, R. K. A. J. Virol. 1977, 23, 227-233.

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Figure 1. Schematic diagram of the fluorescence microscopy method used to isolate a single nanopore: (A) low-porosity polycarbonate membrane with sputtered gold surface film facing up; (B) membrane placed on a drop of FITC solution; (C) FITC solution wicks up through the pores and visualized in the fluorescence microscope; (D) one nanopore chosen and the other pores masked off with a tape mask.

EXPERIMENTAL SECTION Materials. The tracked but not etched polycarbonate membranes were obtained by special order from Osmonics (Bryan, TX). These membranes were 12-µm thick and had a track density (as determined by field-emission scanning electron microscopy after etching the tracks into pores) of 50 tracks cm-2. A membrane with much higher track density (107 cm-2) was also investigated here. This tracked membrane (also 12 µm thick) was obtained from Whatman. Fluorescein isothiocyanate (FITC) was obtained from Aldrich, and a 1 mM solution, dissolved in 1-propanol at pH ) 9.0, was prepared; the pH was adjusted with triethylamine. All other chemicals were of reagent grade or better and were used as received. Purified water was obtained by passing housedeionized water through a Barnstead E-pure model D4641 water purification system. Pore Etching. Etching was done at room temperature (23 °C) by simply immersing the tracked membrane into a glass beaker filled with 100 mL of 6 M NaOH. After the desired etch time, the membrane was removed from the etch solution and immersed into a 1 M formic acid neutralizing solution. The membrane was left in this solution for 1 h and then immersed for 1 h into purified water at 40 °C. The membrane was then rinsed with purified water and stored in air. Isolating a Single Nanopore. A fluorescence microscopy method (Figure 1) employing a Zeiss Axioplan 2 microscope was used. A thin gold film (∼10-nm thick) was first sputtered onto one face of the etched polycarbonate membrane. A 20-µL drop of the FITC solution was placed on a glass microscope slide, and the membrane was immediately placed on this solution drop with the Au film facing upward (Figure 1B). The FITC solution wicked through the nanopores forming droplets (larger than the pore diameter; vide infra) at the upper surface of the membrane (Figure 1C). These solution droplets were visualized via the fluorescence microscope, using an excitation wavelength of 519 nm. To mark an area of the membrane surface containing only a single nanopore the brightfield illumination of the microscope was

adjusted such that only this desired area was seen through the microscope. An extrafine-point Sharpie (Sanford, Bellwood, IL) marking pen was then used to circumscribe the portion of the membrane visible through the microscope. In addition to isolating portions of membranes containing a single nanopore, this method was used to isolate membrane portions containing two, three, and four nanopores. The circumscribed portion of the membrane was then isolated by applying a piece of tape (3M Scotch brand No. 3750) with a 3-mm-diameter hole punched through it. The tape was applied such that the surrounding pores were under the tape, and the selected pore was in the hole (Figure 1D). The membrane was then rinsed thoroughly with 1-propanol to remove all of the FITC dye. The Au film was sputtered on the membrane surface to ensure that only the FITC that has wicked through the pores, and not the solution between the membrane and the glass surface, was seen in the fluorescence image. Field-Emission Scanning Electron Microscopy (FESEM). FESEM was used to measure the diameter of the nanopores obtained. An Hitachi S-4000 FESEM with a resolving power of ∼1.5 nm was used. In addition, FESEM was used to explore the geometry of the pores obtained from the etching process used here. This is a critical issue because it has recently been shown that the pores in the commercially available track-etched membranes are cigar-shaped;20 that is, the pore is cylindrical through most of the membrane thickness but tapers at both membrane faces to conical tips. As per Schonenberger et al.,20 pore shape was investigated by plating Au nanowires in the pores, dissolving the membrane, and imaging the resulting nanowires. Because of the larger number density of nanowires obtained, these analyses were conducted on nanowires plated in the 107 pores cm-2 membrane. The electroless plating procedure described previously14-16 was used to plate the Au nanowires. To obtain solid Au nanowires,15 as opposed to hollow Au nanotubes,14,16 a plating time of 24 h was employed. The plating procedure yields both the nanowires within the pores and Au surface films covering both faces of the membrane. After plating, the Au surface films were removed by mechanically polishing with a cotton swab wetted with ethanol. The membrane was then dissolved by immersion into methylene chloride. The resulting solution was filtered through a branchedpore Anopore (Whatman) 0.02-µm alumina filter membrane to collect the liberated nanowires. The polycarbonate from the dissolved membrane was removed by rinsing the filter with copious quantities of methylene chloride. FESEM images of the Au nanowires were obtained by imaging the surface of the Anopore filter. Gold Nanotube Membranes. We have shown that when short plating times are used, the electroless plating method yields hollow nanotubes (as opposed to solid nanowires) within the pores of such track-etched membranes.14,16 This approach was used here to effectively decrease the inside diameter of the nanopores. A membrane sample with a single 55-nm-diameter pore was electrolessly plated to obtain the corresponding single Au-nanotube membrane. A plating time of 4 h was used. As per the nanowire case, the plating method yielded the Au nanotube within the pore (20) Schoenenberger, C.; van der Zande, B. M. I.; Fokkink, L. G. J.; Henny, M.; Schmid, C.; Kruger, M.; Bachtold, A.; Huber, R.; Birk, H.; Staufer, U. J. Phys. Chem. B 1997, 101, 5497-5505.

plus thin Au surface films covering both faces of the membrane. These surface films do not block the mouths of the nanotube,14,16 and as a result, transmembrane ion currents can be measured without removing these surface layers. Electrochemical Measurements. The membrane sample was clamped between the two halves of a U-tube cell,21 and each half-cell was filled with ∼5 mL of 1 M KCl. (These solutions were unbuffered and had a pH of 6.2.) The resistivity of this 1 M KCl electrolyte was measured using an Accumet AR50 conductivity meter; a value of 13 Ω cm was obtained. A Pt wire (1.0-mm diameter) was inserted into each half-cell solution. For the nanopore membrane experiments (no gold nanotube within the pore), a potentiostat (EG&G 273) was used to apply a constant transmembrane voltage between the Pt electrodes and measure the resulting transmembrane current. Because the applied transmembrane potential was always g1.5 V, the current was carried by reduction of water at one Pt electrode and oxidation of water at the other. Because of the low currents obtained with these nanopore membranes, the water electrolysis reactions did not produce a measurable change in the pH of the half-cell solutions. Charge was carried through the nanopore(s) by migration of K+ and Cl- ions from the contacting solution phases. The same U-tube cell, electrolyte, and electrodes were used for the single Au nanotube membrane experiments. However, because the diameter of the Au nanotube is so small (∼2 nm; see below), the membrane resistance is enormous (>1011 Ω), resulting in pA-level transmembrane currents. These currents are too low to measure with a conventional potentiostat. For this reason, a Kiethley instruments 6487 picoammeter/voltage source with exceLINX software was used to apply the constant transmembrane potential and measure the resulting transmembrane ion current. The protocol used was to step the transmembrane potential to the desired value, monitor the steady-state transmembrane current obtained, and measure this current 10 min after the potential step. A steady-state current is obtained because the large membrane resistance makes the RC time constant of system corresponding large (∼106 s). As a result, there is essentially no decay in the double-layer charging current associated with the potential step over the 10-min time interval used here. Hence, the current measured for the Au nanotube membranes is a purely capacitive current, and Faradic reactions are not needed to depolarize the Pt electrodes. Again, current was carried through the nanotube by migration of K+ and Cl- ions from the contacting solution phases. RESULTS AND DISCUSSION Microscopy. Figure 2A shows a fluorescence microscopy image of a portion of a membrane’s surface that contained only a single nanopore. The pore is observed as a bright green spot (FITC fluorescence) against a totally black background. This pore was obtained by etching the membrane for 10 min. Figure 2B shows a FESEM image of the same pore. Images of this type were used to determine the pore diameter, in this case 30 nm. The spot size in the fluorescence microscopy image is significantly larger (∼2.5 µm), indicating that a droplet of the FITC solution “blossoms” at the membrane surface from the pore. Figure 2C,D (21) Miller, S. A.; Young, V. Y.; Martin, C. R. J. Am. Chem. Soc. 2001, 123, 12335-12342.

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Figure 4. FESEM image of a complete (12-µm long) Au nanowire. Insets show magnified views of the nanowire ends.

Figure 2. (A) Fluorescence microscopy image of a single 30-nmdiameter pore isolated using the procedure in Figure 1. Arrow shows position of the pore. (B) FESEM image of the same 30 nm pore. (C, D) As per (A) and (B) but for a 55-nm-diameter pore.

Figure 3. Pore diameter vs etch time. The circular points are for membranes that had a pore density of 107 pores cm-2. The triangular points are for the 50 pores cm-2 membrane.

shows analogous images for a pore that resulted from an etch time of 30 min. The fluorescence microscopy image shows a FITC spot size of ∼3.6 µm, and the FESEM image shows that this pore is 55 nm in diameter. FESEM analyses of this type were done for membranes etched for times ranging from 10 to 80 min. Because it was easier to find the pores in the FESEM images, most of these analyses were done on membrane samples with 107 pores cm-2; however, to confirm that the relationship between etch time and pore diameter was independent of pore density, analyses were also done on the 50 pores cm-2 membranes (Figure 3). These analyses show that pore diameter is linearly related to etch time, increasing at a rate of ∼2 nm min-1 (Figure 3), independent of pore density. As noted above, it has recently been shown that the pores in commercially available track-etched filter membranes are cigarshaped.20 It has been suggested that this pore geometry arises because the fission fragment that creates the damage track also generates secondary electrons, which contribute to the damage along the track.20 According to this hypothesis, the number of secondary electrons generated at the faces of the membrane is less than in the central region of the membrane, and this is why the pore has a larger diameter in the middle. Because pore shape is critical to any application involving transport through, or 6864

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measurements of ion currents in, these membranes, we have investigated the shape of the pores obtained by our etching process. Figure 4 shows a FESEM image of a typical Au nanowire that extended through the entire thickness of the polycarbonate template membrane; i.e., the length of the nanowire is equivalent to the thickness of the membrane, 12 µm. Such images show that the nanowires have a constant diameter (in this case 55 nm) down their entire length. Most importantly, these images show that conical tips are not present on the ends of the nanowires. (Magnified views of the ends of the nanowires are shown in the insets.) This is in clear contrast to analogous images obtained for Au nanowires plated in the commercially available membranes.20 These results show that the conical pore ends observed in the commercial membrane are not a consequence of the tracking process, as suggested previously,20 but rather occur during pore etching. Apparently, the etching solution used commercially contains additives that slow the rate of etching at the membrane surface. Electrochemical Measurements. Assuming that the ionic resistivity (F) of the electrolyte within a nanopore is the same as the resistivity of the bulk electrolyte solution, the ionic resistance of a single nanopore (Rp) can be calculated from the pore diameter (dp) and the pore length (l) via

Rp ) 4Fl/dp2π

(1)

The pore length is simply the thickness of the membrane (12 µm). If the membrane sample contains N nanopores of diameter dp instead of a single pore, then the net resistance of the sample (Rm) is given by

Rm ) 4Fl/Ndp2 π

(2)

Assuming that each pore acts as a perfectly ohmic resistor, then the ionic current flowing through the membrane sample (i) is related by Ohm’s law to the applied transmembrane potential difference (∆E). Combining Ohm’s law with eq 2 gives

i ) (∆E)Ndp2π/4Fl

(3)

Figure 5. Transmembrane ion current vs number of pores in the membrane sample. Points are experimental data. Line is calculated on the basis of the FESEM-determined pore diameter of 55 nm.

Figure 6. Transmembrane ion current vs applied transmembrane potential for a single-nanopore membrane with FESEM-determined pore diameter of 55 nm. Points are experimental data. Upper (dashed) line calculated for pore diameter of 55 nm. Lower (solid) line calculated for pore diameter of 53 nm.

To test eq 3 membrane samples etched for 30 min were prepared with 1, 2, 3, and 4 nanopores in the sample. FESEM images showed the pores in such membranes were 55 ( 3 nm in diameter. Figure 5 shows a plot of i vs the number of nanopores in the sample for an applied transmembrane potential difference of ∆E ) 1.5 V. In agreement with eq 3, a linear relationship (correlation coefficient ) 0.996) is observed. If the FESEMdetermined average pore diameter (55 nm) is used in eq 3 to calculate the i vs N data, the solid line in Figure 5 is obtained. There are no adjustable parameters in these calculations, and the fit between the experimental and simulated data is excellent. These results confirm that the bulk solution resistivity value is applicable for the electrolyte in these 55-nm-diameter pores. Because 55 nm is large relative to the diameters of the hydrated ions (∼0.3 nm),22 this was the expected result. We will have more to say about pore vs bulk-solution electrolyte resistivity below. Equation 3 also predicts that i for a membrane sample is linearly related to magnitude of the applied transmembrane potential, ∆E. Figure 6 shows data of this type for a singlenanopore membrane etched for 30 min. In agreement with eq 3, good linearity (correlation coefficient 0.998) is obtained. However, if the average FESEM-determined pore diameter (again, 55 nm) is used to calculate the i vs -∆E plot, the upper dashed line in Figure 6 is obtained. Good agreement between the experimental and calculated data are observed at low values of ∆E, but the experimental data lie below the calculated (dashed) line for ∆E values greater than ∼4 V (Figure 6). (22) Freiser, H.; Fernando, Q. Ionic Equilibria in Analytical Chemistry; John Wiley & Sons: New York, 1963; p 25.

Figure 7. Transmembrane ion current vs applied transmembrane potential for a single Au nanotube membrane. The points are the experimental data. Three calculated lines are shown corresponding to nanotube diameters of 2.0, 1.9, and 1.8 nm.

If dp is used as an adjustable parameter in eq 3 to fit the experimental and simulated data, excellent agreement is obtained for dp ) 53 nm (lower solid line in Figure 6). This electrochemically determined dp is more accurate than the FESEM value (55 nm) because the FESEM value is an average over a number of pores and because it was obtained from surface images of the pore mouths only. In contrast, the electrochemical measurement is for the pore in question (i.e., not an average), and it interrogates the pore down its entire length. The high sensitivity of the calculated current to pore diameter results because the current is related to the square of dp (eq 3). Interestingly, the electrochemically determined value is within the standard deviation of the FESEM value, indicating that the electrochemical method is both more accurate and more precise. We will have more to say about the precision of this electrochemical method for determining the pore diameter in the discussion of gold nanotube membranes below. To confirm that the transmembrane current is related to the square of the pore diameter, membrane samples having single pores with diameters ranging from 30 to 140 nm were prepared. The transmembrane current for these membranes was measured at a constant transmembrane potential of 1.5 V. A plot of current vs dp2 is linear (correlation coefficient ) 0.9996), and the experimental data fall on the line calculated from the FESEMdetermined pore diameter values (data not shown). Note that this does not contradict what is said above because the discrepancy between the FESEM dp value and the measured current was not observed in Figure 6 until the transmembrane potential exceeded ∼4 V, and only 1.5 V was used for the i vs dp2 analysis. A Single Au Nanotube Membrane. For many of the applications that we envision for these single-nanopore membranes (e.g., stochastic sensing),1-4 it is essential that the pore diameter approaches molecular dimensions. We have already shown that this can be accomplished by electrolessly plating Au nanotubes within the pores of such membranes.14,16 However, this prior work involved commercially available membranes with pore densities greater than 108 cm-2. Au nanotubes have not been plated previously in single-nanopore membranes. A membrane sample containing a single 55-nm-diameter pore was electrolessly plated for 4 h to yield a Au nanotube within the pore. Figure 7 shows a plot of ion current vs applied transmembrane potential for this single-nanotube membrane sample. As would be expected from Analytical Chemistry, Vol. 75, No. 24, December 15, 2003

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eq 3, this plot is linear (correlation coefficient ) 0.999) and passes through the origin. We have used a gas-flux method to determine the inside diameter of Au nanotubes plated in the commercially available membranes.14,16,23 This is not possible here, because the gas flux through a single nanotube would be immeasurably low with our apparatus. However, we can use gas-flux data obtained for nanotubes plated in the high-pore-density, commercially available membranes to approximate the nanotube inside diameter for this single-nanotube membrane. Figure 2 in our previous paper 23 shows a plot of nanotube inside diameter vs plating time for Au nanotubes plated within the pores of a commercially available membrane with nominally 30-nm-diameter pores. A careful analysis of the pores in this membrane24 has shown that the cylindrical part of the pore that runs through most of the membrane thickness is 55 ( 4 nm in diameter, identical with the diameter of the single-nanopore membrane used here. A plating time of 4 h in this commercial membrane yields nanotubes with an inside diameter of 2 nm.23 The solid lines in Figure 7 were calculated from eq 3 using nanotube diameters of 2.0, 1.9, and 1.8 nm. The first point to note is the remarkable agreement between the nanotube diameter obtained from the best-fit electrochemical data (1.9 nm) and the diameter obtained from the gas flux measurement on Au nanotubes in the commercial membrane (2 nm).23 However, implicit in this apparent agreement is the assumption that the resistivity of the electrolyte confined within these nanotubes is not appreciably different from that of the resistivity of the bulk solution. We will have more to say about this point in the Conclusions. The second point to note from Figure 7 is, again, the sensitivity of the calculated transmembrane current to nanotube diameter. Least-squares analysis on the experimental data in Figure 7 gives a slope and standard deviation of the slope of 2.31 ( 0.01 pA V-1. As indicated in Figure 7, this slope provides a nanotube diameter of 1.9 nm. The slope of the lines calculated assuming a nanotube diameter of 2.0 and 1.8 nm are 2.62 and 2.12 pA V-1, respectively. These slope values fall well outside the boundaries of the standard deviation of the slope of the experimental data, meaning that we can reliable distinguish our experimentally determined apparent diameter of 1.9 nm from diameters of 2.0 and 1.8 nm. CONCLUSIONS We have demonstrated a new method for isolating single nanopores in track-etched membranes. Using this method, we have obtained membrane samples containing from one to four nanopores with diameters, determined using FESEM, ranging from as small as 30 nm to as large as 200 nm. Ion current measurements were used to confirm and refine the FESEM diameters. We have also shown that a Au nanotube can be electrolessly plated within the single nanopore. As has been shown in our prior work, this provides a route for closing down the diameter of the nanopore to molecular dimensions.16 Good agreement was obtained between the inside diameter determined electrochemically for a single-nanotube membrane (1.9 nm) and the inside diameter determined from a gas-flux measurement on an analogous high-nanotube-density membrane (2 nm). These data (23) Jirage, K. B.; Hulteen, J. C.; Martin, C. R. Anal. Chem. 1999, 71, 49134918. (24) Gasparac, R.; Mitchell, D. T.; Martin, C. R. Electrochim. Acta, in press.

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suggest that the electrochemical method provides a convenient way to determine the inside diameter of a nanotube in a singlenanotube membrane. This is important because the previously used gas-flux method is not applicable to the single-nanotube case. There is, however, a caveatsthe electrochemical method makes the assumption that the resistivity of the electrolyte confined within the nanotube is the same as the resistivity of the bulk electrolyte, and this raises the question under what conditions is this assumption valid? A good starting place for exploring this issue is the vast literature on ionic currents in naturally occurring ion channels; Hille provides a comprehensive review of this literature.25 These channels are water-filled pores with inside diameters that can be less than 1 nm. Hille points out that the activation energy for ion transport in some ion channels is equivalent to the activation energy for ion transport in a bulk aqueous electrolyte solution.26,27 This would suggest that the ionic conductivity of the electrolyte in the channel is equivalent to that of the bulk electrolyte. However, this agreement may be fortuitous and may reflect the evolutionary need to make ion transport in channels as rapid as possible. The ionic migration term of the Nernst-Planck equation also provides a good starting point for exploring this issue.28 This equation relates the flux of an ion due to migration (Jm, mol s-1 cm-2) in an electric field (dE/dx) to the diffusion coefficient for the ion (D), the concentration of the ion (C), and the charge on the ion (z):

Jm ) -(zF/RT)DC(dE/dX)

(4)

The question then becomes how does confinement within a nanoscopic pore affect the various terms of this equation? It is well-known that when the diameter of a pore becomes comparable to the diameter of the diffusing species, the diffusion coefficient within the pore decreases relative to the bulk solution valueshindered diffusion.29 Theory predicts that for a pore with a diameter of 2 nm and ions of diameter 0.3 nm, the pore diffusion coefficient should be about half of the bulk-solution D value.29 Equation 4 would suggest that this would lower the flux of the ion in the pore relative to bulk solution. This diminution in D was recently observed in molecular dynamics simulations of ion transport in nanopores.30 However, despite this drop in the pore D, the simulation predicts that the ionic conductivity of the electrolyte in the nanopore can be higher than the bulk-solution value. For example, the simulation predicts that for a nanopore that has a diameter 6.7 times larger than the diameter of the electrolyte ions (as is the case for our ∼2 nm-diameter nanotube), the conductivity within the pore is ∼1.6 times higher than the bulk-solution conductivity.30 The authors explain that this is due to a decrease in the electrostatic interactions between the ions in the nanopore. At lower values of the ratio of the nanopore-to-ion (25) Hille, B. Ion Channels of Excitable Membranes, 3rd ed.; Sinauer Associates: Sunderland, MA, 2001. (26) Hille, B. Ion Channels of Excitable Membranes, 3rd ed.; Sinauer Associates: Sunderland, MA, 2001; p 51. (27) Hille, B. Ion Channels of Excitable Membranes, 3rd ed.; Sinauer Associates: Sunderland, MA, 2001; p 366. (28) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, 1st ed.; John Wiley & Sons: New York, 1980; p 27. (29) Deen, W. M. AIChE J. 1987, 33, 1409-1425. (30) Tang, Y. W.; Szalai, I.; Chan, K.-Y. Mol. Phys. 2001, 99, 309-314.

diameters (i.e., smaller diameter nanopores), the conductivity became dramatically lower than the bulk-solution value, as might be expected from the effect of hindered diffusion on the magnitude of D. The other factor to be considered is the concentration of ions in the nanopore. One of the most interesting effects in this regard concerns ion concentrations in nanopores that have fixed charge along the pore walls. (In Cl--containing electrolytes, our Au nanotubes are negatively charged.31) Theory predicts that if the nanopore radius is comparable to the thickness of the electrical double layer at the pore wall (clearly the case for a 2-nm-diameter nanotube), the total ion concentration within the nanopore can be higher than in the electrolyte solution in contact with the nanopore.32 This is because counterions must be incorporated into the nanopore to neutralize the surface charge on the pore wall. Hence, one could envision a case where the hindered diffusion diminution in D is compensated for by the electrostatic enhance(31) Nishizawa, M.; Menon, V. P.; Martin, C. R. Science 1995, 268, 700-702. (32) Cervera, J.; Manzanares, J. A.; Mafe, S. J. Membr. Sci. 2001, 191, 179187.

ment in C (eq 4) and the conductivities of the electrolyte in the nanopore and the bulk solution are the same. The bottom line is that the relationship between the conductivity of the electrolyte in a nanopore and the conductivity of the bulk electrolyte is a complicated issue. Our nanotubes provide a unique opportunity to experimentally explore this issue. If one borrows from the ion-channel literature, one avenue for investigating how pore diameter affects electrolyte conductivity is to measure the activation energy of the conductivity in the nanopore. We will have more to say about this in future publications. ACKNOWLEDGMENT This work was supported by the National Science Foundation and the Office of Naval Research. The authors acknowledge valuable discussions with Prof. Hagan Bayley of Texas A&M University. Received for review June 3, 2003. Accepted September 22, 2003. AC034602N

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